Mehmet Baran

Completely Regular Objects and Normal Objects in Topological Categories

In this paper, various generalizations of the usual completely regular spaces and completely normal spaces to topological categories are given. Moreover, the relationships among various forms of these generalizations are investigated.

Compactness, Perfectness, Separation, Minimality and Closedness with Respect to Closure Operators

In this paper, the characterization of closed and strongly closed subobjects of an object in categories of various types of filter convergence spaces is given and it is shown that they induce a notion of closure. Furthermore, each of the notions of compactness, perfectness, separation, minimality and absolute closedness with respect to these two new closure operators are characterized in these categories and some known results are re-obtained.

Closure Operators in Convergence Spaces

We define two closure operators of some well-known topological categories and investigate the relationships between these closure operators and the one that is given in [9]. As a consequence, we characterize separation properties T0, T1, and T2 for these well-known categories and compare them with the ones that are given in [3] and [6]. Finally, we characterize the epimorphisms in the subcategories of these given categories.

CONDITIONS IMPLYING CONTINUITY OF MAPS

In this paper, we generalize the notions of preserving and strongly preserving maps to arbitrary set based topological categories. Further, we obtain characterizations of each of these concepts as well as interprete analogues and generalizations of theorems of Gerlits at al (20) in the categories of filter and local filter convergence spaces.